Because you're walking on the Overland, you're not technically allowed to do that route in April.
Bookings are required for each walking season (1 October to 31 May).
This is supposed to explain how it works during the booking season:
http://www.parks.tas.gov.au/file.aspx?id=37489"Bushwalkers intending to use part of the OLT, and who do not pay the Overland Track Fee, should, in most cases, not walk more than one overnight segment."
It's somewhat limiting unfortunately.
EDIT: By limiting, I mean that going in via the Arm River Track to Pelion - for example - then up to the Never Never and looping back is further than an overnight segment and thus not allowed. But, if you go in reverse I think that is allowed. That may be why many of the blogs are the way they are (ie from Junction Lake to the Falls)